Welcome to Seunghun Lee(이승훈)'s Math page!

Hello! I am a postdoc (Research Assistant Professor, funded by BK 21) at Department of Mathematical Sciences at KAIST.

Previously, I was a postdoc at Hebrew University of Jerusalem from August 2022 until January 2024, under the supervision of Prof. Eran Nevo and Prof. Gil Kalai. Before that, I was a postdoc at Binghamton University (SUNY Binghamton) from 2020 Fall where I worked with Prof. Michael Gene Dobbins. Prior to it, I was a graduate student at KAIST under the supervision of Prof. Andreas Holmsen.

I am interested in combinatorial properties of geometric objects. These include, but are not restricted to, combinatorial properties of simplicial complexes such as transversal numbers and coloring, combinatorial convexity and its topological extension, rainbow problems, and order types (or oriented matroids).

Email: seunghun (dot) math (at) kaist (dot) ac (dot) kr

CV

Education and Positions

• (current) Postdoc (Research Assistant Professor, funded by BK 21), Department of Mathematical Sciences, KAIST, South Korea. Feb. 2024 -.

• Postdoc, Einstein Institute of Mathematics, Hebrew University of Jerusalem (under Prof. Eran Nevo and Prof. Gil Kalai), Jerusalem, Israel. Aug. 2022 - Jan. 2024.

• Postdoc (Robert Riley Visiting Assistant Professor), Department of Mathematical Sciences, Binghamton University (SUNY Binghamton), New York, USA. Sep. 2020 - Jul. 2022 (Mentor: Prof. Michael Gene Dobbins).

• Ph.D. in Mathematical Sciences, KAIST, South Korea, Aug. 2015 - Aug. 2020 (Advisor: Prof. Andreas Holmsen).

• Exchange student to Tokyo Institute of Technology via Campus Asia, under the guidance of Prof. Tamás Kálmán, Oct. 2015 - Feb. 2016.

• M.S. in Mathematical Sciences, KAIST, South Korea, Mar. 2014 - Aug. 2015 (Advisor: Prof. Andreas Holmsen).

• B.A. in Economics & B.S. in Mathematics, Yonsei University, South Korea, Mar. 2006 - Feb. 2013 (Aug. 2007 - Jul. 2009: Military service at the ROK Army).

Publications

Papers/Preprints

• S. Lee and Eran Nevo. On colorings of hypergraphs embeddable in R^d. preprint. (2023) (arXiv)

• Michael Gene Dobbins and S. Lee. Inscribable order types. Discrete & Computational Geometry. (2023) (arXiv)

• Joseph Briggs, Michael Gene Dobbins and S. Lee. Transversals and colorings of simplicial spheres. Discrete & Computational Geometry. 71 (2024), 738–763. (arXiv)

• Andreas Holmsen and S. Lee. Leray numbers of complexes of graphs with bounded matching number. Journal of Combinatorial Theory, Series A. 189 (2022), Article 105618. (arXiv)

• Tamás Kálmán, S. Lee and Lilla Tóthmérész. The sandpile group of a trinity and a canonical definition for the planar Bernardi action. Combinatorica. 42 (2022), 1283-1316. (Arxiv)

• Andreas Holmsen, Minki Kim and S. Lee. Nerves, minors, and piercing numbers. Trans. Amer. Math. Soc. 371 (2019), 8755-8779. (Arxiv)

• S. Lee and Kangmin Yoo. On a conjecture of Karasev. Computational Geometry: Theory and Applications. 75 (2018), 1-10 (Arxiv)

• Andreas Holmsen and S. Lee. Orthogonal colorings of the sphere. Mathematika 62 (2016), 492 - 501. (Arxiv)

Other manuscripts

• Ph.D. Thesis: Topology of complexes of graphs with bounded matching number, 2020. (link)
  In the paper, Linusson, Shareshian, and Welker considered the homotopy type of the non-matching complex of a graph G when G is either a complete graph or a complete bipartite graph. In this thesis, we consider an analogue scenario which  focuses more on vanishing homology groups but a given graph G is not limited to complete graphs or complete bipartite graphs. That is, we prove the near Leray property of the non-matching complex of a graph G. This topological result implies a sufficient condition for the existence of a rainbow matching. This work is an extended version of the paper ``Leray numbers of complexes of graphs with bounded matching number".

• Master Thesis: Combinatorial geometry on the sphere, 2015. (link)
  In this thesis, we prove some new results on colorings on the sphere and oriented matroids. For colorings on the sphere, we first give a slightly different, but essentially same result as in the paper ``Orthogonal colorings of the sphere". As the consequence of the proof, we prove the conjecture given by Jonathan Noel. For oriented matroids, we first prove a generalization of Theorem 2 in the paper ``Points Surrounding the Origin" to the oriented matroid version. Next, we prove a version of Ham-Sandwich theorem for oriented matroids.

Presentations

• IBS Discrete Math Seminar, IBS Discrete Mathematics Group, Daejeon, South Korea. Nov. 20, 2023.

• Haifa Workshop on Interdisciplinary Applications of Graphs, Combinatorics and Algorithms, University of Haifa, Haifa, Israel. June 20, 2023.

  • Transversals and colorings of geometric hypergraphs: simplicial spheres and hypergraphs embeddable into R^d

• KU-Jerusalem Lunch Seminar, Hebrew University, Jerusalem, Israel. Dec. 15, 2022.

• HUJI Combinatorics Seminar, Hebrew University, Jerusalem, Israel. Oct. 24, 2022.

• IBS Discrete Math Seminar, IBS Discrete Mathematics Group, Daejeon, South Korea. Aug. 1, 2022.

• REU seminar (organized by Prof. Peter Johnson), Auburn University, Auburn, AL, USA, Jul. 14, 2022.

• Auburn University Combinatorics Seminar, Auburn University, Auburn, AL, USA, Mar.24, 2022. 

• Spring Eastern Virtual Sectional Meeting (Special Session on Discrete and Convex Geometry), Mar. 19-20, 2022.

  • Transversals and colorings of simplicial spheres (with Joseph Briggs and Michael Gene Dobbins)

• Cornell Discrete Geometry and Combinatorics Seminar,  Cornell University, Ithaca, NY, USA, Feb.21, 2022. 

• IBS Discrete Math Seminar, IBS Discrete Mathematics Group, Daejeon, South Korea. Jan.4, 2022.

• AMS Special Session on Topological Methods in Discrete Mathematics, Nov. 20-21, 2021.

  • Transversals and colorings of simplicial spheres (with Joseph Briggs and Michael Gene Dobbins)

• Math and Cookies, SUNY New Paltz, New Paltz, NY, USA, Feb.24, 2021. 

• Combinatorics Seminar, Binghamton University, Binghamton, NY, USA, Nov.10, 2020.

• IBS Discrete Math Seminar, IBS Discrete Mathematics Group, Daejeon, South Korea. Apr.28, 2020. (link)

• The 94th KPPY workshop, Postech, Pohang, South Korea. Nov.9, 2019.

• CoSP workshop and school on topological methods, Charles University, Prague, Czech Republic, Jul.22-26, 2019.

• Mini workshop before the KPPY workshop, Yeungnam University, Gyeongsan, South Korea, Dec. 14, 2017.

• Topology Seminar, Tokyo Institute of Technology, Tokyo, Japan, Jan. 13, 2016.

• JCDCG^2 2015, Kyoto University, Kyoto, Japan, Sep. 14-16, 2015.

  • Orthogonal colorings of the sphere (with Andreas Holmsen)

• OSACA seminar, Pusan National University, South Korea, Apr. 23, 2015.

Teaching experience

As Instructor @ Binghamton University

• Spring 2022 : Graph theory (MATH381).

• Fall 2021 : Differential/Integral Calculus (MATH224/225), Discrete Mathematics (MATH314).

• Spring 2021: Number Systems (MATH330).

• Fall 2020: Linear Algebra (MATH304), Discrete Mathematics (MATH314).

As Teaching Assistant @ KAIST 

• Spring 2020: Probablity and Statistics (CC511).

• Fall 2019: College Mathematics (MAS100).

• Spring 2019: Introduction to Linear Algebra (MAS109).

• Fall 2018: College Mathematics (MAS100).

• Spring 2018: Calculus I (MAS101) (I received the outstanding TA award).

• Winter 2017-2018 Online T.A.: College Mathematics (MAS100) (for the Bridge Program).

• Fall 2017 Tutor: College Mathematics (MAS100) (for international students).

• Spring 2017: Calculus I (MAS101), Discrete Geometry (MAS478).

• Fall 2016: College Mathematics (MAS100), Linear Algebra (MAS212).

• Spring 2016: Calculus I (MAS101), Discrete Mathematics (MAS275).

• Spring 2015: Discrete Mathematics (MAS275).

• Fall 2014: Calculus II (MAS102).

(last updated: Feb.7.2023.)